310-2301/01 – Mathematics 1 (Math 1)
| Garantující katedra | Katedra matematiky a deskriptivní geometrie | Kredity | 5 |
| Garant předmětu | RNDr. Jan Kotůlek, Ph.D. | Garant verze předmětu | RNDr. Jan Kotůlek, Ph.D. |
| Úroveň studia | pregraduální nebo graduální | | |
| | Jazyk výuky | angličtina |
| Rok zavedení | 2019/2020 | Rok zrušení | |
| Určeno pro fakulty | FMT, FBI, FAST, FS, HGF, FEI | Určeno pro typy studia | bakalářské |
Cíle předmětu vyjádřené dosaženými dovednostmi a kompetencemi
After completing this course, students should have the following skills:
* Use rules of differentiation to differentiate functions.
* Sketch the graph of a function using asymptotes, critical points.
* Apply differentiation to solve problems.
* Solve a system of linear algebraic equations.
* Work with basic objects in three dimensional Euclidean space.
Vyučovací metody
Přednášky
Individuální konzultace
Cvičení (v učebně)
Anotace
I. Calculus.
Function of one variable (basic notions, inverse function, elementary functions);
Limits and Continuity of a function;
Differentiation of a function (differentiation rules, application, L'Hospital's rule).
II. Linear algebra.
Vector spaces;
Matrices and determinants;
Systems of linear algebraic equations (Gaussian elimination, Frobenius theorem).
III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).
Povinná literatura:
Doporučená literatura:
Forma způsobu ověření studijních výsledků a další požadavky na studenta
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-elaborate programs,
-pass the written tests,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points.
Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
E-learning
http://www.studopory.vsb.cz (in Czech)
Další požadavky na studenta
Další požadavky na studenta nejsou.
Prerekvizity
Předmět nemá žádné prerekvizity.
Korekvizity
Předmět nemá žádné korekvizity.
Osnova předmětu
1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems.
Podmínky absolvování předmětu
Výskyt ve studijních plánech
Výskyt ve speciálních blocích
Hodnocení Výuky
Předmět neobsahuje žádné hodnocení.